-LRB- CNN -RRB- -- Twelve suspected members of the Zetas drug gang and a member of Mexico 's Navy were killed in a shootout on an island in a lake that straddles the U.S.-Mexico border , authorities said Monday .

The Mexican Navy said the shootout occurred Sunday on Falcon Lake , located between Texas and the Mexican state of Tamaulipas , after troops patrolling the area spotted a camping area on an island .

The suspected drug traffickers used the island for storing marijuana to be transported by boat to the United States , the Navy said in a statement .

After the shootout , the Navy said it seized guns , ammunition and bullet-proof vests from the island .

Falcon Lake drew the attention of law enforcement authorities on both side of the border last September after an American man on a personal watercraft was reportedly ambushed by attackers and shot in the head .

2010 : ` He took a bullet for me , ' Falcon Lake victim 's wife says

Tiffany Hartley told police that she and her husband were riding water scooters on the lake on September 30 when they were attacked .

Her husband 's body has not been found , and the case has remained unsolved .

`` It did n't happen in the United States , '' said Zapata County , Texas , Sheriff Sigifredo Gonzalez .

Suspects in Falcon Lake killing identified

And Mexican authorities , he told CNN last month , have `` somewhat of a zero solvency rate , and a zero conviction rate . ''

`` So unfortunately , this case may remain open forever , even though the information and the evidence may be there , '' according to Gonzalez .

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Mexico 's Navy says a shootout occurred around an island used to store marijuana

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Twelve suspected members of the Zetas drug gang and one member of Mexico 's Navy are killed

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Falcon Lake is between Texas and the Mexican state of Tamaulipas

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It drew attention last year after an American was reportedly shot there